Activated solids: Spontaneous deformations, non-affine fluctuations, softening, and failure

Technical Deep Dive: Activated Solids

Overview

This work investigates spontaneous deformations in active solids by quantifying local rearrangements through non-affine fluctuations relative to global strain. The researchers found that:

• The global non-affinity grows quadratically with active speed and linearly with persistence before saturating, in contrast to simple active-temperature estimates.
• At higher activity, the local non-affinity distribution develops bimodality, reflecting the coexistence of rare large rearrangements and predominantly small fluctuations. This coexistence precedes the divergence of non-affinity and serves as a precursor to defect proliferation and eventual melting.
• Spatial correlations of non-affinity exhibit a correlation length that grows with active speed and persistence before saturating, while the relaxation dynamics are set by the persistence time.
• Activity-induced softening reduces the shear modulus and destabilizes both solid and hexatic order, with two-step melting mediated by proliferation of topological defects.
• Spatially patterned activation provides a direct route to locally induce non-affinity and mechanical softening.

Methodology

The researchers modeled the active solid as an ensemble of 2D Active Brownian Particles (ABPs) interacting via the Weeks-Chandler-Andersen potential. They defined a non-affine parameter to quantify local rearrangements relative to global strain, and performed scaling analysis and numerical simulations to study its behavior as a function of activity parameters.

Results

1. Scaling of global non-affinity:
   • Mean non-affinity grows quadratically with active speed and linearly with persistence before saturating.
   • Excess non-affinity due to activity scales as <X^(a)>/a_ρ ~ Λ^ν, with ν ≈ 2.0.
   • The density-dependent prefactor a_ρ ~ (ρ - ρ_0)^-1, where ρ_0 reflects activity-induced softening of the solid.
2. Coexistence of small and large non-affinities:
   • At high activity, the distribution of local non-affinity develops bimodality, with a secondary peak at large values.
   • This coexistence of small and rare large non-affine rearrangements precedes divergence of non-affinity and defect proliferation.
3. Spatial and temporal correlations:
   • The non-affine correlation length increases with active speed and persistence before saturating.
   • The relaxation of system-averaged non-affinity is governed by the active persistence time.
4. Structural changes and melting:
   • With increasing activity, the shear modulus decreases, and both solid and hexatic order are destabilized.
   • Melting occurs via a two-step process, with the proliferation of topological defects.
5. Locally induced non-affinity and softening:
   • Spatially patterned activation can directly induce non-affinity and mechanical softening in localized regions of an otherwise passive solid.

Interpretation

The observed scaling of global non-affinity reflects the distinct mechanisms by which activity drives particle rearrangements in solids. Increasing self-propulsion enhances active fluctuations, while increasing persistence promotes more coherent local rearrangements. The coexistence of small and large non-affinities signals the onset of defect formation and melting. Spatial and temporal correlations reveal the collective nature of rearrangements induced by activity, in contrast to the isotropic, homogeneous displacements in equilibrium solids.

The activity-induced softening and destabilization of solid and hexatic order, as well as the ability to locally control non-affinity, have implications for the design of adaptive metamaterials and the dynamic regulation of rigidity in biological systems.

Limitations & Uncertainties

• The study is limited to 2D active solids; extension to 3D systems may reveal additional phenomena.
• The researchers did not explore the role of temperature (passive thermal fluctuations) in the dynamics of active solids.
• The proposed mechanism for locally inducing non-affinity, while experimentally feasible, has not been directly demonstrated.

What Comes Next

Future work could investigate:

• The interplay between activity and thermal fluctuations in 3D active solids.
• The role of specific particle interactions and geometries in determining the mechanical response.
• Experimental validation of the local activation approach to control non-affinity and softening.
• Applications of activity-induced mechanical control in adaptive metamaterials and biological systems.

Sources:

• Activated solids: Spontaneous deformations, non-affine fluctuations, softening, and failure